Art De La Guerre

[Ramses II]

Using Cards instead of “dice” for AdlG
An alternative option to using Average dice.

Background
I don’t know about other people, but I often have games that depend more on the dice thrown than the skill of the players involved, and which can easily be upset if there are an excessive consecutive sequence of high or low number dice thrown, or if there is an unusual distribution of numbers through the game. This is a suggestion to remove these excesses.

The idea is to ensure that all numbers are evenly distributed through the game (although there may be groupings of the same number appearing at times during the game). It is NOT playing “cards”, but merely a means to reduce the excessive distribution of numbers.
To illustrate this, last Monday Andy threw seven consecutive “1”s in a game of AdlG against Simon, and a fortnight ago I had a game with Ian which lasted 5 turns and in which I threw 87 dice. Instead of the ~14.5 of each number, I threw the following:-
14x “6”
15x “5”
20x “4”
12x “3”
8x “2”
18x “1”

Although the average dice number is 3.55, the median point of those thrown (the true middle point of the dice values) was 4.01. Basically I was getting above average dice - very unusual for me - or more accurately I was getting very few “2”s and lots of “1”s and “4”s.

By contrast recently I had a game of AdlG with Alan which lasted over seven turns, in which we both managed to “throw” over 120 dice, each using a deck of 24 cards that were reshuffled over four times. During this game we both had 20 of each number and because the decks had four of each card, we could not have a sequence of more than 4x any card.
(Conceivably the last cards revealed could appear on the top of the shuffled deck – see note below)

The theory
The probability of each number appearing is 1/6. All well and good. But chance is random, so the next throw could result in the same number appearing, and the next – though the chance of this same number continuing to appear is increasingly remote. If one were to throw a dice a million times, you might expect to see each number come up approximately the same number of times, so the distribution of the number, the amount of times it appears, should be roughly the same or 1/6 of the whole.

If we take six cards 1-6 and pick one at random the chance of any number coming up is the same, 1/6. However that number has been “used” and cannot be picked again until the deck is reshuffled. By not shuffling the deck, we can ensure that the numbers are fully ‘distributed’, unlike my game against Ian.

If we calculate that a game lasts roughly 120 dice throws, we could create a deck that contained 120 cards with 20x each of 1-6 on the assumption that the deck would just about run out as the game finished. This would give a fully ‘distributed’ deck of numbers where each player would have the correct amount of the numbers 1-6 at his disposal. However this approach has a number of problems;

• The game could end prematurely so the distribution of numbers would then be incomplete leaving us with the same situation as with dice; some numbers will have appeared more often than others.
  
• The cards would also become fully ‘random’ so the distribution of the numbers is just as uneven as with dice; there is nothing to stop all the “1”s being shuffled together.

Alternatively we could use a ‘deck’ of just 6 cards. This presents different problems

• While the distribution of the numbers becomes ‘perfect’; ie they appear an equal number of times, they are almost not random (apart from being mixed up in six cards).
  
• The ‘deck’ requires frequent shuffling, which is rendered awkward by the limited number of cards available.

Since reducing the size of the deck also reduces the randomness of the numbers, which is undesirable, the ideal approach seems to be where the ‘deck’ of cards can be reused (shuffled) a limited number of times before the game ends in order to ensure that the numbers are evenly distributed (ie will appear an equal number of times in the game), yet which are also sufficiently random within the deck. Using the deck twice (ie shuffling once) may not distribute the numbers sufficiently evenly. However, if we consider 120 throws as a reasonable game length, then the deck should ideally be between a quarter and a third of that number, or between 30 to 40 cards.

Given that we are using the numbers 1-6, the ideal ‘deck’ used by each player should be 36 cards. This will be slightly more random than a quarter of the anticipated number of throws while still giving a good distribution of six groups of numbers, which should reduce the potential problems (see notes below)

The method
The basic steps are:-

1. Take three card packs, split into two ‘decks’ of red and black cards numbered 1-6, giving two ‘decks’ of 36 cards (although we could drop one set of 1-6 to give the exact 30 card “quarter deck”).
   
2. Shuffle and place the decks face down to one side by each player, one using the ‘red’ deck, the other using the ‘black’ deck.
   
3. Every time a dice would be thrown, turn over a card instead. This includes checking for initiative, terrain placement, flank marches, etc. Where this is for shooting or melee, reveal the cards simultaneously.
   
4. To reduce the potential abuses, the players must agree to process all shooting and melees in the same direction each turn. ie from the same edge of the battlefield

Notes
There are several points to note here

• It is possible though highly unlikely that a run of numbers at the end of the ‘deck’ could be followed by a run of the same numbers at the start of the shuffled deck. This would be the equivalent of throwing the same number many times, but the difference is that the distribution of the numbers would still be even throughout the game.
  
• The higher the number of 1-6 sets, the greater the randomness of the system. Five sets would be an exact quarter, six gives greater randomness which I think seems to be the ideal.
  
• The individual ‘decks’ can be expanded to 42 cards approximating to the 40 card “third deck” (needing 3.5 card packs). Doing this will increase the likelihood of an uneven distribution if the game ends early, though it also increases the randomness of the deck. (this could also make the end of the game more likely to coincide with the end of a deck which might be beneficial).
  
• The greater the number of cards also means that the end of the game is not likely to coincide with the end of the deck, which in turn makes card counting less effective.
  
• People might consider 'card counting' could be detrimental. I have not found this to be the case to date, especially where players agree to "play from the left", because it becomes hard to arrange things in both decks to the advantage of one player, especially across several shuffles.
  
• Splitting the cards into red and black suits is really usefull visually, and permits players to place their card by their units as and when necessary.
  
• Cards by their very nature are much easier to see than dice.

The whole point of this approach is that the numbers provided are still random, yet they are also distributed evenly throughout the game, avoiding the extreme craziness of ‘luck’ that we all experience.

• The benefit of this approach is that excessive degrees of random luck are removed, bringing out a greater reliance on skill.
  
• However it does remove the excuse that a player won / lost ‘because of appalling dice’ . . . .

[vexillia]

Very interesting post. It's easy enough to implement as you only need three packs of cards.

I'm not sure about some of the nomenclature & there seems to be inconsistencies in the use of random and distribution. There are three serious maths points to make:

[1] The cards can never be truly random because the card values are dependent. The possible outcomes are restricted by the size of the deck (unlike dice) and the extent of restriction/dependency increases as the deck becomes spent irrespective of the size of the deck.

[2] If you've rolled a string of sixes the chance of rolling another one is always 1 in 6. The probability does not increase as the series grows because each roll is deemed to be independent and therefore does not depend on anything that went before (unlike cards). Now if you were calculating the odds of rolling a given series before any dice have been rolled then the odds do lengthen with the length of the series. Best not to confuse the two.

[3] 120 dice is not a large number. Your expectation of a flat distribution for all scores from such a small number of dice is unfounded. I've done a similar analysis with over 1,000 dice and it still wasn't even. See this animation and this one too.

Nonetheless I am intrigued and will see if I can talk someone into trying this in a game sometime soon.
_________________
Martin Stephenson

[thierry.b]

3 decks of playing cards ordered. I'll try that soon.
Merci
_________________
Mes figs

[Commodore]

In order to avoid any predictability and keep some suspense :
A possibility could be for each player to use a 48 card deck (8 of each), re-useable during the game
At the beginning, deck is shuffle and the first 8 cards are set aside.
When the deck is running out, it is shuffle again, 8 cards are withdrawn and so on…
_________________
"Damn the torpedoes, full speed ahead"
Cdr Farragut,Mobile 1864

[madaxeman]

I also play Malifaux, which used a card-based system instead of dice to generate combat outcomes.

Even with a standard 52-card deck it is entirely possible to "count cards" - the trick is you do not need to count everything, just (in an ADLG case) the "5's and 6's" (doesnt matter which is which, just add up all of the 5s and 6s you see).

Even with a 48 card deck that only means you need to be able to count up to 16.

By the time you get to the bottom half-dozen or so cards you will have a pretty good idea how many 5's and 6's are going to come up in your last few cards - and plan your combats accordingly.

That's why dice are better IMO
_________________
www.madaxeman.com

[A4]

Hi - thought I'd posted, but it does not seem to have come up. Apologies if this is a repeat.

I have tried this with Ramses and it works very well.

I think it is quicker than dice. The only slight delay is shuffling. That can be sped by having the non-active player shuffle the dead cards when the pack is near to finishing and then just shuffling-in the last few cards used.

Personally, I do not think that luck plays much part in ADLG. How would the same people keep winning if it did?

Nor is randomness bad. Real battles were pretty random. The ability to exploit good fortune / hedge against bad was a test of generalship. One of the reasons why reserves tended to play a greater part in real battles than they do on the table (under almost all sets, not just ADLG) is that our battles are more predictable than the real thing.

Of course, cards do not entirely balance things out. Your elite knight might draw (and "waste") a 6 when fighting my over-lapped light horse. I might draw a 6 in a key fight with a general.

But cards do tend to even things out. The main advantage of this is that it causes us to think less about luck and more about tactics. Sometimes I blame mistakes on the dice and then repeat the errors, hoping that different rolls will produce a different outcome. Knowing that you and your opponent will have "rolled" pretty-well the same same total over the course of the game encourages us examine our play more closely.

Alan

[A4]

On card counting. I know there are people out there with extraordinary memories. I wonder why they'd be wasting them on wargames when they couldd be winning money at cards, but I guess they mean that this system might not be ideal for competitions.

However, for friendly evening games - and particularly for ones in which you want to try out a new army or tactic - I don't think it is a problem. As Ramses says, if all shooting and all melees start at the side of the table nearest the window the advantage gained by knowing what cards will emerge is minimal. It would help when deciding whether to commit a general to melee. I guess that if they knew they had a run of good cards coming horse archers might charge rather than shoot. But the 99 percent of us without photographic memories have only a certain number of brain cells to commit to the game. Cells used counting cards would be more productivley employed annalysing the position / trying to remember the rules.

Alan

[Ramses II]

Hi all, and thanks for the comments

Vexilla, I am not a mathematician, so please forgive my poor explanations. The point is that you can reduce the chance of picking a card by increasing the size of the deck which in my terms increases the ‘randomness’ of the deck. However doing this reduces the number of times that you shuffle the deck, which can result in the numbers being distributed less evenly - numbers can be grouped together at one point in the deck and the player must then wait for the next shuffle for those numbers to recur. So over the 120 ‘dice throws’ numbers can become grouped together rather than being spread relatively evenly. 

This brings me to Commodore’s post. Using eight groups increases the decks to 48 cards. This allows a possible run of eight cards of a single value, and at most only two shuffles in a game - creating a deck where the numbers are likely to be less evenly distributed across the game. 

Finally to Madaxman and A4 on card counting. I agree that it is possible to do this, but am not sure that it necessarily has a big impact - providing people adopt the same process each turn.

Although players may think that their deck is ‘better’ than their opponent’s at some point in the game, the cards drawn are still random and cannot be completely predicted. Trying to engineer a particular outcome at a particular point using a particular deck (or worse against the opposing deck), becomes almost impossible in my experience due to the nature of the game with the increasing number of key melees and shooting occurring (in a specific predetermined order) towards the end of the game. 
Indeed this is where using the 36 card deck may be slightly better than the 30 card deck because it increases the ‘randomess’ of both decks making card counting slightly less effective.  

Finally, please let us know your experiences if you do try this approach to playing AdlG. 

[Hazelbark]

I like the idea in general.

However I believe the instability of the dice is important. Now perhaps you're system doesn't change what I want.

I think it is IMPORTANT to have luck play a role. I think the more you mitigate luck the more you play to the stronger player.

In a recent game, I had the situation well in hand. An opponent had to decide on a decision to commit impetuous HC against my HI sword or not. They saw the situation for them was one they needed to take a risk. So they charged. I was confident. But in the series of units fighting most went normal distribution but two were adjacent 6-1s. Add in furious charge and I abruptly had a big hole in my line. Under systems that reduce the extreme outcomes that become less probable. I then had to scramble to save the situation. If luck had been median, then my superior battlefield position would have made the game a foregone conclusion. Now the luck of that situation should not have gone against me to that degree, but it is important that it could.

Too much tilting in favor of strong players, will drive off weaker players.

[ethan]

I don't like this idea as I don't really think it achieves much unless you have such a small pool of cards that you can effectively count cards. This would be a terrible idea and counting cards is not really all that difficult...

[Ramses II]

Hmm, I don’t disagree there, and you will note that luck and 6-1 situations can and do still occur, because those cards have not been removed or replaced. 

What this process counters is intensely skewed distributions like those I outlined at the start of the post. This is achieved by shuffling the deck at regular intervals. The more shuffles that occur, the more evenly the numbers become distributed throughout the game.    

The process does remove one dice instability - the annoying habit of the dice falling on the floor and bouncing into inaccessible corners

[Longtooth]

Hi Ramses,

As Tim points out, it would be very easy to count cards. Knowing that I have more sixes in my deck than ones, I would play aggressively.

Jesse

[lionelrus]

I think dice roll is a part of the game.
_________________
"Quand on a pas de technique, faut y aller à la zob"
Perceval à Yvain et Gauvain.

[matisph10]

[madaxeman]